review1 - Review for Exam#1 The exam is on Wednesday...

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Review for Exam #1The exam is on Wednesday, February 29, 2012. Calculators may be used.Questions will reflect the emphasis of examples done in class, and quiz andhomework questions.TopicsThe exam will cover the following sections of the text:Functions: 0.1–0.6.The derivative: 1.1–1.4, 1.6–1.8.Applications of the derivative: 2.1–2.7.Review questions for exam #1(1) Letp(x) =x5-2x+ 1 and letq(x) = (x3+ 2)2. Compute(a)q(-1)(b)q(a+b)(c)p(q(-1))(d)q(p(x))(2) Find the equation of the straight line through the points (5,4) and(7,0).(3) Find the points of intersection of the curvesy=x3+2xandy= 3x2.(4) Using the definition of the derivative as a limit, computef0(x) iff(x) =x2-3x+ 2.(5) Find the equation of the tangent line toy=x2-3x+ 2 at the pointwherex=-1.(6) Find the derivatives of the following functions. You do not have tosimplify your answers.(a)f(x) =x3+ 2x2+ 3x+ 4.(b)f(x) =78x(c)f(x) =x3+ 2x23(d)f(x) = (x-2)(x+ 2)(e)f(x) = ((6x+ 5)4+ 3)2(7) Letf(x) =13x3-32x2+ 2x+ 4. Find the regions on which(a)fis decreasing(b)fis concave up(8) Sketch the graph of

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